Universit`a degli Studi di Milano-Bicocca

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Universit`

a degli Studi di Milano-Bicocca

Dipartimento di Fisica

Ph.D. Thesis

OPTIMIZATION AND CHARACTERIZATION OF PET

SCANNERS FOR MEDICAL IMAGING.

Giacomo Cucciati

Supervisor:

Prof. Marco Paganoni

Corso di Dottorato in Fisica e Astronomia Ciclo XXVI Settore Scientifico Disciplinare FIS/07

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Abstract

Positron emission tomography is an imaging technique that appeared to be a valid instrument for cancers detection and neuro-imaging studies. Since first models built during 1960s, an incredible effort has been done by researchers to develop scanners more and more advanced with higher specificity and efficiency. Monte Carlo simulations have shown to be a very important tool during design phase of PET prototypes thanks to their ability to simulate systems with many coupled degrees of freedom, as it happens when particles interact with matter. This Thesis work has started in the frame the Crystal Clear Collaboration when the EndoTOFPET scanner was already under development. This prototype is an high spatial resolution scanner for the study of pancreatic carcinoma and prostatic cancer, composed by a PET head mounted on an ultrasound endoscope and a PET plate to be placed outside the body. The Collaboration has chosen to use Monte Carlo simulations to support the design of this project and two simulations toolkits were available: Geant4 and SLitrani. In this work both the toolkits are studied and ray tracing in scintillator crystals are tested. In particular photon extraction efficiency is simulated under different surface treatments as coating and wrapping. Also the influence of the crystals geometry on light output is tested simulating different scintillators sections and lengths. Both Geant4 and SLitrani have shown to give similar results under these conditions. A main issue was observed regarding secondary particles since Geant4 is able to simulate their production while it is not possible with SLitrani. On other hand crystals anisotropy for optical photons can be activated in SLitrani. Light yield

measurements were performed in laboratory on LYSO and PbWO4 crystals to have

a comparison with the results obtained by mean of simulations. Good agreements are obtained for what regards surfaces treatments while more tuning was required to simulate the effect of surface imperfections and diffusion inside crystals.

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Acknowledgement

In my opinion this is always the most difficult part to write at least as the title. This is the reason I keep it at last. Every time I am worried to forget someone, to be too concise (the opposite is impossible) or too vague. Apparently it is not even possible to write down just a list of names... So let’s start in the old fashioned way and I hope that will be enough!

First of all I want to thank my supervisor, Marco, for the opportunity he gave me to work on this project and in particular to work inside the CERN walls. Even if I lived a very small part of what this international organization can offer it was a great experience! For this reason I want to thank also the Crystal Clear Collaboration and all its members (the ones I met at least). In particular, a thank to Etiennette, key figure of what showed to be a very good team. Avoiding a long list of names of all the people I have worked with, a special thank to the RS task force, that means: Ben (I hope I have been a good office colleague for him), Aron (the beer guy) and Milan (most of the time a voice in the headphones)! And of course I want to thank also the Italian group (too many!), colleagues and friends outside the walls of the office. I really don’t like to list all of them, so lot of thanks to Marco and Nicolas for their help in this work and I let them spread the word to the other guys... To be honest a double thank to Marco and Alessio for the revision of my Thesis.

I have already written too many lines and my family will understand if I stop here. I will have the opportunity to thank them in person. I hope that the same will be with all the other people I mentioned and who I don’t.

Almost a page... not bad.

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List of Figures

2.1 Neuronal activity can be easily studied by mean of a PET scanner

and the injection of FDG in the body. . . 4

2.2 A scheme of how the PET technique works, from the decay of the

radiofarmaceutical to the elaboration of the final image. . . 6

2.3 A typical photopeak and Compton edge acquired with a scintillator

crystal used in a PET device. . . 7

2.4 A scheme of how true, scattered and random coincidences are generated. 7

2.5 Scheme of the parallax error computed when no DOI information is

collected. . . 10

2.6 Scheme of the functioning of a photomultiplier. . . 10

2.7 Some PET models . . . 11

2.8 Scheme of advantages/disadvantages in using 2D and 3D mode. . . . 12

2.9 The room were ClearPEM-Sonic have been installed at Hopital Nord.

The Aixplorer is in the foreground, ClearPEM in the background. . . 14

2.10 Results obtained with different imaging devices . . . 16

2.11 A scheme of the EndoTOFPET functioning with the details of the

probe and the external plate. . . 17

2.12 A scheme of the advantages of the experimental d-SiPMs tested by

the research group. . . 18

3.1 Scheme of the bands structure theory. . . 20

3.2 Scheme of the energy levels involved in competitive non-radiative

phe-nomena. . . 23

3.3 Scheme of the displacement of the wave normal, of the field vectors

and of the energy in an electrically anisotropic medium. . . 28

3.4 The ellipsoid of the wave normals. Construction of the directions of

vibrations of the D vectors belonging to a wave normal s. . . 29

3.5 Double refraction: construction for permissible wave normals. . . 31

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5.1 Example of one of the 20 histograms obtained collecting the distances

travelled by optical photons in a LSO crystal. . . 42

5.2 Reflectivity comparison between G4 and SL with polished crystals. . 44

5.3 Reflectivity comparison between G4 and SL applying different crystal

surface treatments. . . 44

5.4 Reflectivity comparison between G4 and SL applying different crystal

surface treatments. . . 45

5.5 Light output comparison between G4 and SL with naked crystals. . . 47

5.6 Light output comparison between G4 and SL applying specular

treat-ments. . . 48

5.7 Light output comparison between G4 and SL applying diffusive

treat-ments. . . 48

5.8 Light output comparison between G4 and SL with naked crystals. . . 49

5.9 Light output comparison between G4 and SL applying specular

treat-ments. . . 50

5.10 Light output comparison between G4 and SL applying diffusive

treat-ments. . . 50

5.11 Energy deposition profile along a LSO crystal with a 511 keV source

applied. . . 51

5.12 Trasversal energy deposition profile along a LSO crystal with a 511

keV source applied. . . 52

5.13 Number of optical photons collected in the first 100 ps after the

gamma interaction with crystal. . . 52

5.14 Photon extraction efficiency of PbWO4crystal in isotropic and anisotropic

configuration. . . 54

5.15 Experimental set-up. . . 55

5.16 Example of a spectrum obtained. . . 57

5.17 An example of a signal profile obtained during measurements of LYSO

crystals. . . 58

5.18 Chart of the LY values. . . 59

5.19 Chart of the LY values for the 2×2 mm2 _{series with wrapped crystals. 61}

5.20 Chart of the LY values for the 2×2 mm2 and 3×3 mm2 series with

grease applied to crystals. . . 62

5.21 Plots of the LY ratios extracted from the simulations. . . 63

5.22 Plots of the LY ratios extracted from the measures. . . 63

5.23 Comparison of LY extracted from the measures and simulations. . . . 64

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5.25 Comparison of LY extracted from the measures and simulations. . . . 65

5.26 Spectrum obtained with a 6 min. long acquisition of the light output of the 1.9 cm length PbWO4 crystal. The red line shows the fit applied to the photopeak. . . 67

5.27 Light yield values of the 4 PbWO4 samples; error is evaluated to be 5% of the measurements. . . 67

5.28 Light yield averaged values of the 4 PbWO4 samples. . . 68

6.1 One of the detectors configuration I have simulated. The S11828 SiPM imposes own constraints on plate crystals pitches. . . 73

6.2 Graphical scheme of the method applied for the DOI calculation. . . 74

6.3 ”Kill All” algorithm to chose coincidences in singles lists files. . . 76

6.4 A scheme of the probe coupled with the external plate and the point source placed between them. . . 77

6.5 A scheme of the two plates with a point source placed in the middle at 20 cm from the internal surfaces. . . 78

6.6 Reconstruction of the 1 mm source, No DOI. . . 78

6.7 Reconstruction of the 1 mm source, with DOI. . . 79

6.8 Reconstruction of the 1 mm source . . . 79

6.9 Scheme of the planar and the curved plate designed for the EndoTOF-PET scanner. . . 80

6.10 Sensitivity calculated for different plate configurations, some theoret-ical geometries have been added as comparison. . . 81

6.11 Scheme of analysis chain used for my simulations, from generation of data with Geant4 to the reconstruction algorithm. . . 82

6.12 Schemes of two possible SiPM models, candidates for crystals plate matrices. . . 82

6.13 Plot of the sensitivity values obtained testing two possible SiPM mod-els and different crystals lengths. . . 83

6.14 Schemes of three possible SiPM models, candidates for crystals plate matrices. . . 84

6.15 Sensitivity values of different SiPM models. . . 85

6.16 Spatial resolution along Z axis for different SiPM models. . . 86

6.17 Spatial resolution along X axis for different SiPM models. . . 87

6.18 Simulation of a multifocal source in a background noise volume. . . . 88

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6.20 Transverse (left) and coronal (right) view for the 141.4, 212.1 and

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List of Tables

2.1 Table of the most common radioisotopes used in medical imaging. . . 8

3.1 Properties table of the most common scintillation materials. . . 26

5.1 Student’s t-test results applying different absorption lengths-energies couples for the LSO crystal. . . 42

5.2 Student’s t-test results and significance level obtained applying dif-ferent surface treatments to the boundary surface LSO-air. . . 43

5.3 Dimensions of crystals simulated for the light output comparison by SL and G4. . . 47

5.4 Student’s t-test results and significance level. . . 48

5.5 Student’s t-test results and significance level. . . 50

5.6 LY values for the 2×2 mm2 _{and 3×3 mm}2 _{series with naked crystals.} ₅₉ 5.7 LY values for the 2×2 mm2 _{series with wrapped crystals by Teflon.} _. ₆₀

5.8 LY values for the 2×2 mm2 and 3×3 mm2 series with grease applied to crystals. . . 61

5.9 Light yield values for the four samples measured expressed in ph/MeV. Four sets of measurements were taken. . . 66

6.1 Spatial resolution and sensitivity simulated in EndoTOFPET and two-plates configurations. . . 79

6.2 Elements tested during the simulations. . . 83

6.3 Probe elements not modified during the simulations. . . 83

6.4 Plate elements not modified during the simulations. . . 84

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List of abbreviations

ADC: analog digital converter.

APD: Avalanche photodiode. BGO: Bismuth-Germanate-Oxide. CCC: Crystal Clear Collaboration.

CeF3: Cerium Fluoride.

CERN: European Organization for Nuclear Research. CMS: Compact Muon Solenoid.

CS: coincidences sorter.

CT: computerized tomography. CTR: coincidence time resolution.

d-SiPM: digital silicon photo-multipliers. DAQ: data acquisition.

DOI: depth of interaction.

ECAL: Electromagnetic Calorimeter. EM: electro-magnetic.

ET: emission tomography. FDG: fluorodeoxyglucose. FOV: field of view.

FWHM: full width half maximum. G4: Geant4.

LHC: Large Hadron Collider. LOR: line of response.

LSO: Lutetiumoxyorthosilicate.

LYSO: Lutetium Yttrium Oxyorthosilicate. MC: Monte Carlo.

MPPC: multi-pixel photon counter. MRI: magnetic resonance imaging. NaI: Sodium Iodide.

PET: positron emission tomography. PMT: photomultiplier tube.

ROI: region of interest.

PbWO4: Lead Tungsten Oxide.

PSF: point spread function.

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SL: SLitrani.

SPAD: single-photon avalanche diode.

SPECT: single photon emission computed tomography. STD: standard deviation.

STR: single time resolution. TOF: time of flight.

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Chapter 1 INTRODUCTION

1.1 Thesis overview

During my master degree studies I used Monte Carlo simulations software for physics applications. They play an important role in this sector, thanks to their ability to predict particles behaviour under defined conditions and they are greatly used from the biggest high energy physics experiments to the smallest radiation detectors. My interest for simulation software has brought, thanks to my Tutor, to conceive the guide lines for this Ph.D. thesis. Working side by side with physicists of the Crystal Clear Collaboration at CERN, I had the opportunity to study in deep how Monte Carlo simulators work and I was able to support the developing of an innovative PET scanner, an international project started in the frame of the CCC. My thesis follows the steps of the work I conducted during these three years of my Ph.D.:

• in Chapters 2 and 3, I will briefly explain the groundwork of how PET scanners work and the theory of scintillator crystals. It should act as support to better understand the analysis I have conducted and explained further in the thesis. A section is dedicated to the CCC projects I worked in;

• Chapter 4 is an introduction to Monte Carlo simulations and to the software I have studied, Geant4 and SLitrani. I will try to explain with more details how these software handle optical photons and ray tracing in crystals;

• in Chapter 5, I show the analysis I conducted on Geant4 and SLitrani and their comparison, with a particular attention to light yield measurements and anisotropic crystals;

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• eventually conclusions are reported in Chapter 7.

1.2 Crystal Clear Collaboration, a technology

trans-fer.

Crystal Clear Collaboration [1] was founded in 1990 at CERN. Its activity was fo-cused on the study and development of scintillator crystals to be used as particles detectors in physics experiments related to LHC [2]. In this collaboration experts coming from different disciplines as material science and instrumentation for parti-cle detection were grouped to work side by side, creating a world wide community of about 250 scientists. One of the main goal achieved by CCC during the first

years was the study of the PbWO4 scintillators and the decision in 1994 to apply

these crystals to the electromagnetic calorimeter of CMS [3]. Knowledge acquired in this period naturally flowed in medical imaging applications where scintillators crystals were already applied for PET and SPECT scanners. Less bulky scanners, higher spatial resolution and lower energy particles are some of the different working conditions to which crystals have to be adapted from LHC to medical application. New scintillator materials and new technologies for particles detectors were studied by the collaboration and, once formed a background experience, the collaboration has started some international projects in medical imaging. Milestones of the col-laboration:

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Chapter 2 POSITRON EMISSION

TOMOGRAPHY

2.1 The technique

Positron emission tomography (PET) is a technique belonging to a main branch of medical imaging called emission tomography (ET) which uses radioactive materi-als to image properties of the body’s physiology [4]. Another technique based on the same main principles is single positron emission tomography (SPECT). Images from a PET exam can represent, for example, the spatial distribution of properties such as glucose metabolism, blood flow, and receptor concentrations. Thus, emis-sion tomography can be used to detect tumours, locate areas of the heart affected by coronary artery disease, and identify brain regions influenced by drugs. ET is categorized as a functional imaging approach to distinguish it from methods such as X-ray computed tomography (CT) that principally depicts the body’s architectural structure (anatomy).

2.1.1 The tracer

The main agent of the PET technique is the tracer. It must play two roles: move inside the patient’s body in order to reach the physiological parts to investigate and emit an unique signal that can be received by an external detector and identify its position. At the same time without harming the patient himself.

Some radionuclides show to be good candidates because:

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Figure 2.1: Neuronal activity can be easily studied by mean of a PET scanner and the injection of FDG in the body.

• their nuclear decay produces a characteristic gamma emission that can exit the human body with a low probability of being absorbed and so be received and recognized by an external detector;

• they can be included in some molecules that are normally present in physio-logical processes and so reach specific organs or follow particular metabolisms;

• they are safe for human body from a chemical point of view.

One of the most used radiochemical compound is the 18F-fluorodeoxyglucose

(18F-FDG). It is a tracer for measuring glucose metabolism and it consists of two

components: FDG (similar to glucose) and a fluorine-18 label (18_{F) that permits}

to detect the tracer by counting the gamma-ray emissions it produces. 18_F-FDG

enters cells in the same way as glucose, but it is metabolised by the cell to create a new compound (a metabolite) that remains trapped within the cell. Therefore, the concentration of the radioactive metabolite grows with time in proportion to

the cell’s glucose metabolic rate. In this way, injection of 18_{F-FDG into the body}

allows to form images depicting local levels of glucose metabolism. 18F-FDG is a

valuable tool for brain imaging because the glucose metabolism is related to the

regional level of neuronal activation (Figure 2.1). In recent years, 18F-FDG has

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2.1.2 PET analysis

Some radionuclides belong to the class of decay β+_{. This process can be outlined}

by the following equation:

p → n + e++ ν

where a proton of the atomic nucleus is converted in a neutron with the emission of a positron and an electronic neutrino which leaves the decay zone undisturbed due to the negligible interaction probability [5]. Positrons behaviour is different: as they travel through human tissue, they loss their kinetic energy principally by Coulomb interactions with electrons. Because the rest mass of the positron is the same as the electron, positrons may undergo large direction deviations at each Coulomb inter-action and they will follow a tortuous path through the tissue. When the positrons reach thermal energies, they interact with electrons by the formation of a hydrogen-like orbiting pair called positronium. Positronium is unstable and eventually decays,

via annihilation, into a pair of anti-parallel 511 keV photons (emitted at 180◦

rela-tive to one another). The PET analysis is based on this decay family to estimate the radionuclide distribution inside the patient body. In fact if both emitted gammas are intercepted by two different detectors, it could suppose that the annihilation hap-pened somewhere along the line they have followed (called LOR, line of response). But if more than one atom decays in the same area, it is possible to collect inter-secting LORs and, generally speaking, the higher the concentration of tracer in a specific point the larger the number of intersections. During a PET exam a large number of gamma couples is collected all around the body since the tracer diffuses in the circulatory system but, as mentioned before, areas with an higher concentra-tion of radionuclides will appear. Applying mathematical algorithms based on the previous assumption to the data collected it is possible to recognize and reconstruct graphically these areas with a very good spatial resolution (see Figure 2.2).

For this reason a tracer meant to be used in PET analysis has the further

charac-teristic that the radionuclide decays β+. In the example of the18F-fluorodeoxyglucose,

the fluorine isotope decays in a oxygen atom with the typical emission of a positron and a electronic neutrino as shown in the following schema:

18 9 F → 18 8 O + e +_{+ ν} e

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Figure 2.2: A scheme of how the PET technique works, from the decay of the radiofar-maceutical to the elaboration of the final image.

possible to create a LOR. If not, the first signal is rejected. The electric signal is proportional to the energy released in the detector by the gamma and after an acquisition cycle the system is able to create an energy spectrum with all the data collected. This spectrum shows a characteristic shape: a peak around 511 keV and an edge at lower energies (see Figure 2.3).

In fact, even if all the annihilation gammas are created with 511 keV, only some of them will convert the whole amount into a signal. Along the path from the decay position to the detector, photons can interact with the electrons of the medium they cross (patient body) and partially lose their energy (the collision will change also the direction of the gammas themselves). Moreover a photons can cross the detector without releasing all its energy. It means that, if detected, they will create a signal lower than 511 keV. Applying an energy window to these spectra it is possible to extract only gammas belonging to the photopeak and generate the coincidences LORs with them.

2.1.3 Coincidence events

Figure 2.4 illustrates three kinds of coincidence events that the device accepts: • true coincidences: both gamma rays detected come from a single decay and

they have not scattered in the patient;

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Channel 1000 2000 3000 4000 5000 Counts 0 500 1000 1500 2000 2500 3000 2x2x10 LYSO crystal

Figure 2.3: A typical photopeak and Compton edge acquired with a scintillator crystal used in a PET device.

Figure 2.4: A scheme of how true, scattered and random coincidences are generated. The crystals ring array is a very common configuration in PET devices because it has

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Isotope Half Life (min) Emax (keV) Rangemax (mm) 18_F _109.8 ₆₆₃ _2.6 11_C _20.3 ₉₆₀ _4.2 13_N _9.97 ₁₂₀₀ _5.4 15_O _2.03 ₁₇₄₀ _8.4 82_Rb _1.26 ₃₂₀₀ _17.1

Table 2.1: Table of the most common radioisotopes used in medical imaging.

• random coincidences: two gamma coming from two separate decays but hap-pened simultaneously (or almost).

The goal in PET imaging is to measure and reconstruct the distribution of true coincidences while minimizing the scattered and random coincidences because they carry wrong information of the place where the decay happened. Note that both true and scattered events are referred as prompt events because they come from the decay of a single nucleus and, thus, the gamma rays are detected together. Random, or accidental, coincidences occur if two separate decays are close enough in time to look like a single decay to the system electronics. The prompt rate (trues + scatters) is related linearly to the activity in the patient. However, the randoms rate increases as the square of the activity in the patient and becomes more dominant at higher activity levels. Increasing the number of true coincidences leads to less noise in the image and an higher spatial resolution of the distribution of decay events in the reconstructed image is obtained. Since scattered events carry lower energy than true coincidence, as explained before, most of them can be easily rejected by energy spectra analysis.

2.1.4 Intrinsic spatial resolution limits

The spatial resolution of PET imaging is limited by the fundamental nature of positron annihilation [7]. Although the radial distribution of annihilation events is sharply peaked at the origin (site of positron creation), a calculation of the radius that includes 75% of all annihilation events gives a realistic comparison of the impact of the maximum positron energy on the spatial resolution of PET imaging. Table 2.1 lists the major emitters used in PET imaging, along with positron energy and range in water.

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the 511 keV photons that is approximately 4 mrad (0.23◦) [6]. This is referred to as non-collinearity. A third significant factor limiting PET spatial resolution is the intrinsic spatial resolution of the detector. The resolution of a single detector is often quantified by the full width at half-maximum (FWHM) of the position spec-trum obtained for a collimated point source placed before the detector at a fixed distance from it. The coincidence detector-pair resolution is normally specified as the FWHM of the point-spread function (PSF) obtained from the convolution of the two individual detector PSFs. For a detector composed of small discrete crystals, all interactions are assumed to occur at the center of individual crystals for the purpose of and image reconstruction. As a result, the PSF for such detectors is similar to a step function with a total width equal to the size of a crystal. The coincident PSF is, therefore, a triangular function whose base width is again equal to a crystal size. Thus, the FWHM of the coincident detector PSF is one-half the crystal size.

A final factor affecting PET spatial resolution is referred to as the parallax error, which results from the uncertainty of the depth of interaction (DOI) of the gamma rays in the crystal. Gamma rays may travel unknown distance in the crystal (or adjacent crystals) before being completely absorbed. As a result, if the gamma ray enters the crystal at an oblique angle, the location of the interaction will not be the same as the point of entry into the crystal; the crystal of the interaction may not even be the same as the one first entered (cross-talk event). Thus, unless the DOI within a crystal can be accurately determined, an incorrect line of response (LOR) will be assigned to this interaction because the LOR is normally assigned to a position at the front of the crystal of interaction (see Fig. 2.5). The parallax effect worsens as the source position moves radially away from the center of the scanner because a larger fraction of the gamma rays enter the crystals at oblique angles.

2.1.5 Detector design

The first element of the detection apparatus that a gamma ray strikes is a crystal

material called a scintillator. The scintillator uses energy from the high-energy

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Figure 2.5: Scheme of the parallax error computed when no DOI information is collected.

Figure 2.6: Scheme of the functioning of a photomultiplier.

technique is based on the detection couples of gammas emitted back-to-back by the source, devices show a geometry with a typical cylindrical symmetry.

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Figure 2.7: a) PC-I, the first tomographic PET imaging device. b) A continuous wide

area PET system. c) Advannced GE model. d) A modern PET system for medical

application.

(typically 25 mm thick) or GSO (typically 20 mm thick) arranged in full or partial rings around the patient. Because the NaI(Tl) system use continuous detectors, the axial sampling is determined by the intrinsic spatial resolution of the system and the choice in how the data are collected. These full-ring NaI(Tl) systems are operated exclusively in 3D mode (as explained below) to achieve better sensitivity. Rings in discrete crystals systems are divided in blocks of matrices where each single unit

can contain for example 6×6 or 8×8 very small crystals (6.25×6.25×30 mm3 _BGO

crystals or 6.7×6.75×25 mm3_{LSO crystals). For these devices the spatial resolution}

depends on the crystal dimension itself so research facilities are developing PET devices that mount crystals with smaller and smaller sections (for spatial resolution thickness has a minor relevance). Some examples are shown in Figure 2.7.

Since each crystal needs a dedicated electronic, acquisition system complexity grows with the crystals miniaturization and sets a technological limits to the

im-provement of spatial resolution. Moreover block detectors generally use smaller

PMTs than designs with continuous crystal so they are more expensive (due to the increased number of PMTs and electronic channels). Discrete crystals systems are equipped with removable axial collimators, allowing the systems to operate in either 2D or 3D mode. The GSO systems do not include axial collimators and only operate in 3D mode, as do the NaI(Tl) scanners.

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Figure 2.8: Scheme of advantages/disadvantages in using 2D and 3D mode.

detected by two scintillators with different axial depth are accepted. Axial collima-tors are able to absorb gammas with incident angles too far from the plane normal and different collimators lengths can be chosen to set how tight is the cut (see Fig-ure 2.8). A system without collimators collects in what is called 3D mode. It offers an increase in sensitivity compared to 2D acquisitions. However, there are some limitations because the increased sensitivity is not uniformly distributed axially and the removal of collimation also increases the number of scattered events detected by the detector array. The removal of the collimation also allows more photons from outside the axial FOV to be detected. This increase in the number of single events detected versus the number of coincidence events detected leads to higher dead time and randoms rates.

2.1.6 Sensitivity improvements

The four major options for improving the number of coincidences read during an exam (the sensibility of the instrument) are:

• Increase the patient dose;

• Use more of the energy spectrum; • Increase solid angle;

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Increasing the patient dose is not a practical approach because higher doses would result in higher radiation exposures for the patient moreover this would be advan-tageous only for fast systems not count-rate limited at high activity levels. One approach to gain sensitivity is to use more of the energy spectrum and accept events with energies below the photo peak. It means to accept scattered gammas as good signals with a consequent degradation in the images spatial resolution. The third method consists of the removal of all axial collimation (3D volume imaging) allowing in this way also coincidences with gammas intercepted by different ring arrays. A typical whole-body ring system can realize an increase in the true sensitivity by a factor of 5 but the penalty is a large increase in the acceptance of scattered pho-tons and increased singles rates from activity outside the field of view (FOV) of the system. So this technique proves to be usefully only for dedicated PET system (as brain imaging) with small rings diameter.

Many research facilities are searching for better scintillators, but it’s not easy to create materials with higher stopping power than bismuth germanate (BGO). The main advantages of new scintillators such as lutetium oxyorthosilicate (LSO), in comparison to BGO, is the combination of high light output and fast decay. BGO-based systems typically use detectors 30 mm deep, which provide approximately 90% detection efficiency for 511 keV gamma rays (therefore, 81% coincidence efficiency). Although 100% detection efficiency would improve sensitivity even further, no sys-tems have yet been built with basic detection efficiency greater than that provided by 30-mm-deep BGO crystals. Developing of scintillation crystals will be discuss in the next chapter.

2.2 CCC projects

This thesis work was conducted in the frame of the Crystal Clear Collaboration. When I joined the research group, it was working on two different projects, ClearPEM-Sonic, a dedicated PEM device with an ultrasound elastography system, and

EndoTOFPET-US, a multimodal imaging technique (PET-ultrasound) for endo-scopic pancreas and prostate exams.

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Figure 2.9: The room were ClearPEM-Sonic have been installed at Hopital Nord. The Aixplorer is in the foreground, ClearPEM in the background.

2.2.1 ClearPEM-Sonic

ClearPEM-Sonic is a multimodal breast imaging device that combines the advan-tage of metabolic PET imaging of a dedicated positron emission mammograph with the morphological and structural information provided by the ultrasound system Aixplorer, developed by the SuperSonic Imagine company (see Figure 2.9). Breast cancer can be considered as the first cancer as occurrence among women (almost 40 cases per 100.000 women per year). Its mortality is 23% of all cancer cases but an early detection can greatly reduce this number [8]. Different techniques are adopted for breast cancer detection as radiography, ultrasound or magnetic reso-nance imaging. Anyway, these modalities present problems mainly due to breast density, since healthy tissues and cancer appear very similar in these cases. Whole-body positron emission tomography is able to provide metabolic information, but high cost and poor spatial resolution reduces its use only as support to the pre-vious ones. ClearPEM-Sonic [9] has been designed and developed to answer these requirements.

The fulcrum of the ClearPEM module is composed by two heads holding the

PET detectors [10], [11]. Each of them consists of 96 matrices of 8×4 2×2×20 mm3

LYSO:Ce crystals with a casing of BaSO4acting as matrix structure and reflector for

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each crystal presents a double readout and depth of interaction information (DOI)

is collected. A 360◦ complete acquisition can be obtained thanks to the rotation of a

robotic platform where the two heads are mounted on and a full 3-dimensional breast image can be reconstructed. A rail allows the movement of the heads closer to the subject maximizing the solid angle coverage while the high interaction probability provided by the high crystal density gives us a high sensitivity. For instance the global detection efficiency in the centre of the plates has been determined to be 1.5% at a plate distance of 100 mm. The correction of the parallax error, through the DOI evaluation, and the small section of the crystals installed make ClearPEM an high spatial resolution PET scanner.

An important task of this project was the realization of a merging software tool. 3D images of the region of interest (ROI) are computed independently by both ac-quisition systems and they can be studied indipendently by physicians. But more interesting is the overlapping of the information carried by the FDG density map and the elastographic map that can help the identification of smaller malignant le-sions. To follow and register the transducer position a magnetic tracking system (by Ascencion Technologies, Burlington, Vermont, USA) was chosen. The software will follow transducer position during an ultrasound acquisition and the data collected will be computed to rotate the 3D image in the PEM reference system [12].

With due approval, a first clinical trial on 20 patients [13] was starded at Hopital-Nord, Marseille. An example that demonstrated ClearPEM potential in breast can-cer diagnosis is reported in Fig. 2.10. During the preliminary exam a multifocal breast cancer was detected in this patient. Two lesions have been revealed by the whole-body PET/CT scanner, one in the left breast and the second close to the ax-illa. Smaller lesions around the first one can be detected only using MRI. The high sensitivity and spatial resolution that ClearPEM can achieve allow the detection of those smaller spots. Unfortunately the second cancerous focus is too close to the thoracic wall and ClearPEM is not able to scan that region since it is out of the detector field of view. Completed the first tests, the clinical was recently moved at the San Gerardo Hospital (Monza, IT) where further tests studies will be performed.

2.2.2 ENDOTOFPET-US

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Figure 2.10: Images obtained using a Siemens Biograph 15 PET/CT (a), and using MRI (b). Figures (c) and (d) show the coronal and sagittal views respectively, of the ClearPEM images obtained with same breast.

high spatial resolution scanner composed by a PET head mounted on a commercial ultrasound endoscope and an outer PET plate to be placed outside the body (see Figure 2.11). Even if the probe is very close to the region of interest, noise from radiopharmaceuticals inside adjacent tissues can not be completely avoid because of the random and scatter coincidences. This problem should be solved using time of flight (TOF) measurements. Time of flight is a technique where time of detection of gammas on both the PET detectors are recorded. Using the difference of these values it is possible to calculate the origin of annihilation along the LOR:

∆x = c · (t1− t2)

2

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Figure 2.11: A scheme of the EndoTOFPET functioning with the details of the probe and the external plate.

project with further improvements. It is made of matrices of 4×4 LYSO:Ce crystals

of 3.5×3.5×15 mm3_{. Each crystal matrix is coupled at the rear side to a 4×4 array}

analog MPPC for a plate total size of 230×230 mm2 _{with 256 matrices or 4096}

crystals. Cross-talk was tested for a typical matrix of the external plate and it is evaluated to be less then 5% of gamma interactions. It can be easily suppressed with a threshold setted to 30 keV The probe is a real challenge because of constraints

that dimensions impose. It is made of thin (0.71×0.71×15 mm3) LYSO:Ce crystals

grouped into a matrix of 9×16 crystals. One such matrix is used for the pancreas probe, two matrices are used for the prostate probe. An EM sensor is added to track the probe position and a cooling system is required to control temperature. It is necessary to obtain a precision on probe positioning of about 0.5 mm to obtain a fine image reconstruction. For the internal probe, a digital silicon photo-multipliers (d-SiPMs) is dedicated to each crystal and coupled to it by mean of an optical light concentrator from one of the small crystal sides. Differently from standard SiPMs the collaboration is studying custom pixelized models that are able to collect 48 time values improving time resolution as Plot 2.12 shows [15]. The main goals of this project is to achieve a 200 ps time resolution and 1 mm as spatial resolution. The collaboration is working also on a dedicated image reconstruction algorithm to manage the asymmetric configuration of the EndoTOFPET scanner.

In collaboration with Aix Marseille Universit´e and Universit´e de Lausanne new

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in-Figure 2.12: A scheme of the advantages of the experimental d-SiPMs tested by the research group.

stance, PSMA is an enzyme expressed by prostate epithelial cells that can be

mod-ified to contain 68_{Ga becoming a very specific tracer for this cancer. Development}

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Chapter 3 SCINTILLATOR CRYSTALS

3.1 Scintillation process

Scintillation is a luminescence (flash of light) induced by ionizing radiation in trans-parent, dielectric media [16]. To explain the behaviour of scintillation process it is necessary to introduce the electronic band theory of a solid (see Figure 3.1). It describes the allowed ranges of energy that an electron within the solid may have and the forbidden ones. The existence of continuous bands of allowed energies can be understood starting with the atomic scale. The electrons of a single isolated atom occupy atomic orbitals, which form a discrete set of energy levels. If multiple atoms are brought together into a molecule, their atomic orbitals split into separate molecular orbitals each with a small energy difference. As more and more atoms are brought together the molecular orbitals extend larger and larger, and energy levels of the orbitals split apart to a finer and finer degree. Eventually, the collection of atoms form a giant molecule, or in other words, a solid. For this giant molecule, the energy levels are so close that they can be considered to form a continuum or band. Band gaps are essentially leftover ranges of energy not covered by any band. The most important bands and band gaps, those relevant for electronics and opto-electronics, are those with energies near the Fermi level:

• the valence band covers the higher energies where an electron is still considered bounded to individual atoms;

• the conduction band is the first range of electron energies where electrons move freely but sill within the atomic lattice of the material;

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Figure 3.1: Scheme of the bands structure theory.

Material can be classified on their band gap. In insulators the energy required to an electron to jump the band gap is relevant, it becomes smaller in semiconductor (in some cases thermal energy can be enough to reach the conduction band) while in conductors the valence and conduction bands are so close to be overlapped and

most energetic electrons are always free to move in the lattice. Described in a

very simple way, scintillation process happens when an electron, previously excited, returns to the valence band releasing an optical photon. But contrary to the photo-luminescence which results from the radiative relaxation of an excited ion, it is composed by a complex chain of phenomena.

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wavelength) in the visible or near visible range, which can be easily detect with current photo-multipliers or photo-diodes.

Scintillators can be divided into two major categories: organic and inorganic scintillators. These two groups differ both in their chemical composition as well as in the physical principles leading to light emission. In organic scintillators, the luminescence process is a consequence of transitions made by free valence electrons that occupy so-called molecular orbitals. It is thus a property of the molecular structure. On the contrary, the luminescence of inorganic scintillators is due to the electronic band structure of the crystal and thus a consequence of the crystalline structure.

During a scintillation process five main stages can be considered [17]. The first one starts with the production of primary excitations by interaction of ionizing par-ticles with the material. For incident particle with very high energy, the excitations are essentially deep holes h created in inner-core bands (associated with core orbitals such as 1s electrons) and hot electrons e in the conduction band. Then, in a very

short time scale (10−16-10−14 s), a large number of secondary electronic excitations

are produced through inelastic electron-electron scattering and Auger processes with creation of electrons in the conduction band and holes in core and valence bands. So at the end of this stage all the starting energy is divided in a electromagnetic shower and the multiplication of excitations is stopped. All electrons in the

con-duction band have an energy smaller than 2Eg (e-e scattering threshold) and all

holes occupy the valence band if there is no core band lying above the Auger process threshold (general case). The second stage is thermalization of electronic excitations: hole and electron will cool their energy by coupling to the lattice vibration modes (with production of phonons) until they reach respectively the top of the valence band and the bottom of the conduction band. They can also be bound and form an exciton whose energy is in general slightly smaller than the band gap energy. The next stage is characterized by the localization of the excitations through their in-teraction with stable defects and impurities of the material. For example, electrons and holes can be captured by different traps or self-trapped in the crystal lattice. Excitons, self-trapped excitons, and self-trapped holes can be formed with emission of phonons. The two last steps are related with migration of relaxed excitations and radiative and/or non-radiative recombinations that lead to scintillation by different channels:

e + h → hν (3.1.1)

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e + h + A → ex + A → A∗ → A + hν (3.1.3)

e + h + A → A1++ e → A∗ → hν (3.1.4)

e + h + A → (A1−) ∗ +h → A + hν (3.1.5)

A → A∗ → A + hν (3.1.6)

where e and h are an electron and a hole, ex an exciton, A an activator ion and hν a photon. The first two processes are the simple recombination of a free electron in the conduction band with a hole in the valence band (or deeper bands) that leads to the emission of a photon. A fast scintillation pulse (in UV energy range) is emitted if a deep hole (in bands closer to the core) recombines with en excited electron, it is the case of core-to-valence luminescence, Eq. 3.1.1. Recombinations of electron and hole sufficiently close to the band gap are more probable in particular if they can bind in the vicinity of specific atoms or lattice defects and form a so-called exciton (Eq. 3.1.2) the emission will be in the visible range. Process 3.1.3. describes the quenching of an exciton by the presence of activator ions, and subsequent excitation of the activator ion followed by the emission. Alternatively, as shown in Eq. 3.1.4 and 3.1.5, electrons or holes can be directly captured by an activator ion, a process competing with the formation of excitons. Finally, activator ions can be directly excited by ionizing radiation (see Eq. 3.1.6). The excited activator ions emit a photon when returning to their ground state.

3.2 Competitive process to scintillation

The scintillation process competes with other non-radiative phenomena that cause a loss of photons output [17]. One of these is called thermal quenching. It can be easily explained by Figure 3.2 where the coordinate Q represents the distance between the ion and the ligands while E is the energy. The two parabolas are the potential curves of the ground state and of one excited state. Both of them show a fine split of the energy levels due to the different vibrational modes. An initial equilibrium distance between the luminescent ion and the ligands increases after the electron relaxation of the excited state. The ion-ligand distance is in general larger in the excited state inducing a parabolas offset (Stoke shift) proportional to electron-phonon coupling. In intermediate and strong electrons-phonons coupling, parabolas show an intersection point that is crossed by higher vibrational levels.

Electrons can reach these vibrational by thermal energy (Eq in the scheme) and

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Figure 3.2: Scheme of the energy levels involved in competitive non-radiative phenomena.

emission. In some scintillators material, room temperature is high enough to enhance this phenomenon and consequently reduce scintillation efficiency. For example BGO

has quantum efficiency of only 0.13 because of thermal quenching while Tl+ _and

Ce3+-doped scintillation crystals are almost immune. Concentration quenching is

another mechanism that competes with the scintillation process. In fact interactions between luminescent centres take place by nonradiative energy transfer but their number increases with the doping material concentration in the crystal. A very

good example is given by CeF3, which has a modest light production in spite of a

very high concentration of Ce3+ _ions.

Light photons travelling in the scintillator material can be reabsorbed by a lumi-nescent centre of the same nature that emitted the luminescence itself. In this case it is called radiative energy transfer and it does not affect light yield because sooner or later light will be remitted (we have a delay in the fluorescence decay). If the luminescent center is different a quenching phenomenon takes place and it become a very important limiting factor. Many kind of absorption centres can be present in crystals such as lattice distortions, point defects, color centres, etc.

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3.3 Time response and light yield

The time shape of the light pulse emitted by the crystal can be represented by the following equation:

I = I0(e−t/T − e−t/T 1) (3.3.1)

where T1 is the time constant describing the population of the optical levels (rise time) and T is the time constant describing their decay. A more complete formula should take into consideration that scintillating materials have two decay time: a fast (or prompt) value representing the fluorescence process and the slow (or de-layed) value for phosphorescence and delayed fluorescence. While the fast compo-nent usually dominates, the relative amplitude of the two compocompo-nents depends on the scintillating material. Times of approximately half a nanosecond are required to populate the levels from which the prompt fluorescence light arises. For the very fast scintillators, the decay time from these levels in only 3 or 5 time grater, even if it can be even one or two order of magnitude different for slower material.

The number of electronic excitation Neh, which are potentially available in the

scintillation process, is expressed by:

Neh = Einc/Eeh (3.3.2)

Where Einc is the energy deposited by the ionizing particle and Eeh the average

energy required to produce a thermalized e-h pair. Eehis not really equal to the band

gap but shows values two-three times Egap. The light production of a scintillator

crystal is called light yield and can be calculated by:

Y = Neh· S · Q (3.3.3)

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3.4 Required properties in scintillator crystals

Scintillator crystals production uses several chemical compositions, each showing different responses under the same ionizing particles. Crystals are chosen depending on the aim of their use in order to fit with their characteristics and also PET imaging devices require scintillators with particular features, as listed below:

• stopping power: materials with high atomic number and density have an higher probability to stop gamma rays (high conversion efficiency) then ”light” mate-rials. It increases the number of detected signals, in this way a smaller crystal is able to obtain the same result of a sample bigger but with less stopping power. At the same time a smaller crystal achieves a better spatial resolution and a reduced the DOI influence for the reasons expressed in Chapter 2. BGO and Lutetium-based crystals are favoured in stopping 511 keV gamma rays; • light yield: a high light yield is also mandatory to improve the energy

resolu-tion, which is essentially limited by photo statistics and electronic noise. In PET imaging a well defined photo-peak allows to reject a more correct number of Compton events (see previously) and to increase the image quality. At the same time light yield must behave linearly with particle energy deposition that can be unequivocally convert in an electric pulse;

• scintillation decay time: a fast scintillator response is required to keep a short dead time that is an higher acquisition rate. Moreover it is possible to reduce the gate time window that brings to a minor random acceptance.

All these properties can not be combine easily in a single crystal. For a long period NaI was very used in medical imaging because its considerable light yield and its easy and cheap production. But its low stopping power, long decay time and the not practical hygroscopy urged scientists to look for other materials. BGO crystals have been developed and introduced in PET devices to compensate for NaI weaknesses. As shown in Table 3.1 BGO has a very high stopping power and conversion efficiency. Unfortunately this material shows a small light yield and a not really fast decay time.

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N aI(T l) BGO LSO GSO LY SO LaBr3

Density (g/cm3₎ _3.7 _7.13 _7.4 _6.71 _7.1 _5.3

Effective Z 51 66 60 64 47

Abs. length 511 keV (cm) 3.0 1.04 1.15 1.42 1.12 2.13

Scint. efficiency (ph/keV) 60 9 25 8 32 61

Scint. efficiency (%) 100 15 75 20 14 175

Energy resolution (%) 7.8 12 9.1 7.91 7.1 3.3

Decay constant (ns) 230 300 42 60 48 35

Hygroscopic Y N N N N N

Table 3.1: Properties table of the most common scintillation materials.

3.5 Anisotropic crystals

In this chapter anisotropy in crystals will be briefly explained. This topic is exten-sively explained in [18] where more details of Maxwell equations and light transmis-sion in materials are also covered.

3.5.1 Anisotropy and optical axes

An anisotropic medium is defined as a material whose electrical excitations depend on the direction of electric field. In general the vector D will then no longer be in the direction of vector E (cit Optics of crystals). It is possible to assume that each component of D is linearly related to the components of E:

       Dx = xxEx+ xyEy+ xzEz Dy = yxEx+ yyEy + yzEz Dz = zxEx+ zyEy + zzEz (3.5.1)

The quantities xx, xy, ... are supposed constant in the medium and they

consti-tute the dielectric tensor. The principle of the conservation of energy requires this tensor to be symmetric so it has only six instead of nine independent components.

The electric energy we can be expressed by:

we= 1 8πE · D = 1 8π X kl EkklEl (3.5.2)

and since we have only 6 terms kl, we can write

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where x, y and z where used instead of corresponding E components. Both terms of the equation must be positive since on the left we have an energy and in this way we obtain the equation of an ellipsoid. It can be always transformed to its principal axes and it is possible to find a coordinate system in the crystal such that the equation of the ellipsoid is in a simpler form:

xEx2+ yEy2+ zEz2 = constant (3.5.4)

In this system of principal dielectric axes the material equations and the expres-sion for the electrical energy take the simple forms:

Dk= kEk (k = x, y, z) we= 1 8π( D2_x x +D 2 y y +D 2 z z ) (3.5.5)

x, y and z are called the principal dielectric constants. They are a constant in

the material but they could have a dependency on the frequency (and consequently the six terms of the dielectric tensor). In the rest of the chapter we will consider only monochromatic waves in order to have fixed values.

Starting from a Maxwell equation applied to a region of space which does not contain currents it is possible to obtain the following relation:

D = n

2

µ[E − s(s · E)] =

n2

µE⊥ (3.5.6)

Where E⊥ is the E component perpendicular to s, the direction of the unit wave

normal and t is the unit vector in the direction of the ray vector S. It shows that in a crystal the energy is not in general propagated in the direction of the wave normal. Moreover E, D and s must be coplanar and orthogonal to H and B as shown in Figure 3.3.

Applying this result to Equation 3.5.5 we obtain for each component

µkEk = n2[Ek− sk(E · s)], (k = x, y, z) (3.5.7)

These are three homogeneous linear equations in Ex, Ey, Ez, that can be satisfied

by non-zero values of these components only if the associated determinant vanishes. This implies that a certain relation must be satisfied by the refractive index n, the vector s and principal dielectric constants. This relation can be derived by writing Equation 3.5.7 in the form

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Figure 3.3: Scheme of the displacement of the wave normal, of the field vectors and of the energy in an electrically anisotropic medium.

Adding the three components with the suitable modifications it is possible to obtain the formula:

s2 x ( 1 n2 + 1 µx ) + s 2 y ( 1 n2 + 1 µy ) + s 2 z ( 1 n2 + 1 µz ) = 0 (3.5.9)

and introducing the phase velocity vp (the velocity of the wave in the direction

of the wave normal)

s2_x v2 p− v2x + s 2 y v2 p − vy2 + s 2 z v2 p − vz2 = 0 (3.5.10) using: vx = c √ µx , vy = c √ µy vz = c √ µz (3.5.11)

This is a quadratic equation in v2

p as can be seen by multiplying Equation 3.5.10

by the product of the denominators. Thus for every direction s there are two phase

velocities vp. The two values ±vpcorresponding to a value vp2are counted as one since

the negative value evidently belongs to the opposite direction of propagation -s. We have the important result that the structure of an anisotropic medium permits two monochromatic plane waves with two different linear polarizations and two different velocities to propagate in any given direction. From Equation 3.5.5 we have:

D2_x x + D 2 y y +D 2 z z = 8πwe or x2 x + y 2 y +z 2 z = 1 (3.5.12)

if we use x, y and z in place of Dx/

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Figure 3.4: The ellipsoid of the wave normals. Construction of the directions of vibrations of the D vectors belonging to a wave normal s.

axes. We call this ellipsoid of wave normal (see Figure 3.4) and it can be used to

find both phase velocities vp. We draw a plane through the origin at right angles

to s. The curve of intersection of this plane with the ellipsoid is an ellipse; the

principal semi-axes of this ellipse are proportional to the reciprocals 1/vp of the

phase velocities and their directions coincide with the corresponding directions of vibrations of the vector D. Trying to determine the two semi-axes of the ellipse we find again

µDk = n2[Ek− sk(E · s)] (k = x, y, z) (3.5.13)

Thus we find that the roots of the determinantal equation for n = c/vp are

proportional to the lengths r of the semi-axes of the elliptical section at right angles to s, and, moreover, that the possible directions of the vector D coincide with the directions of these axes. Since the axes of an ellipse are perpendicular to each other, we obtain the important result that the directions of vibrations of the two vectors D corresponding to a given direction of propagation s are perpendicular to each other and s, D’ and D” form an orthogonal triplet.

It is known that an ellipsoid has two circular sections C1 and C2 passing through

the center and that the normals N1 and N2 to these sections are coplanar with the

longest and shortest principal axes (z and x) of the ellipsoid. These two directions

N1 and N2 are called the optic axes and along them there is only one velocity of

propagation: D can then take any direction perpendicular to s.

3.5.2 Optical classification

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• group 1: Crystals in which three crystallographically-equivalent, mutually-orthogonal directions may be chosen. The crystal is optically isotropic and

x = y = z;

• group 2: Crystals not belonging to group 1 in which two or more crystallographically-equivalent directions may be chosen in one plane. One dielectric principal axis must coincide with this distinguished direction. Crystals are said to be

opti-cally uniaxial and x = y 6= z;

• group 3: Crystals in which two crystallographically-equivalent directions can

not be chosen. Here x 6= y 6= z. Crystals of this group are said to be optically

biaxial.

3.5.3 Light propagation in uniaxial crystals

If we place the optical axis in the z direction (i.e. vx = vy), Equation 3.5.10 becomes

(v2_p− v2 o)[(v 2 p− v 2 e) sin θ 2_{+ (v}2 p− v 2 o) cos θ 2_{] = 0} _with s2_x+ s2_y = sin θ2, s2_z = cos θ2 (3.5.14) θ is the angle between the z axis and wave normal s. The roots of this equation are given by: ( v_p02= v_o2 vp”2 = vo2cos θ 2_{+ v}2 esin θ 2 (3.5.15)

It shows that both shells of the normal surface are a sphere of radius v0_p = vo and

a surface of revolution, an ovaloid. Thus one of the two waves that correspond to any particular wave-normal direction is an ordinary wave with a velocity depending on the angle between the direction of the wave normal and the optic axis. The two velocities are only equal when θ = 0, i.e. when the wave normal is in the direction of the optic axis. The vector D of the ordinary wave (D’ in Figure 3.4) vibrates at right angles to the principal plane, the vector of the extraordinary wave (D”) is in this plane.

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Figure 3.5: Double refraction: construction for permissible wave normals. t − r · s c = t − r · s’ v0 r · (s’ v0 − s c) = 0 (3.5.16)

hence the vectors s’/v0− s/c must be perpendicular to the boundary. In Figure

3.5 it is possible to see that this request is obtained if s’/v’ end point Q’ must be on the normal to Σ through the end point P of the vector s/c. In general the normal to Σ cuts the inverse surface in four points, two of which lie on the same side of the boundary as the crystal. Hence there are two such points and therefore two possible wave-normals directions so that in general each incident wave will give rise to two refracted waves. This is the phenomenon of birefringence or double refraction. Calcite is a good example of this optical effect. The two refracted rays lie in the plane of incidence. sin θi sin θ0 t = c v0 sin θi sin θt” = c v” (3.5.17)

Where θi, θ0t and θt” are the angles which the incident and the two transmitted

waves make with the axis. Each of the transmitted waves obeys the same law of refraction as in the case of isotropic media. However, the velocity v now depends on

θt, so that the determination of the direction of propagation in the crystal is more

complicated. In a uniaxial crystal one sheet of the inverse wave-normal surface is a sphere, so that the phase velocity of one the transmitted waves is independent of

θt, this being an ordinary wave. In the case of normal incident (θi = 0) one has

θ0_t= θt” = 0 and both wave normals in the crystal coincide and are in the direction

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Chapter 4 MONTE CARLO SIMULATION

SOFTWARE

4.1 Introduction: Monte Carlo simulations

Monte Carlo methods include a large number of computational algorithms that use the repeated extraction of random numbers to obtain numerical results. They are often used in physical and mathematical problems and generally speaking when the solution of a problem depends on a great number of variables. If their values or probability distributions are known, it is possible to weight the random extraction and fit the algorithm to the specific case. For instance, systems with many cou-pled degrees of freedom are fluids, strongly coucou-pled solids, particles interactions physics and cellular structures. Probably the best example to mention goes back to 1946 when physicists at Los Alamos Scientific Laboratory were working on radiation shielding for neutrons. One of the people of the collaboration was Stanislaw Ulam who had the idea to solve this problem applying the Monte Carlo Method. From his memories:

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differential equations into an equivalent form interpretable as a succession of random operations. Later I described the idea to John von Neumann, and we began to plan actual calculations.” [19]

This project required a code name since it was secret and Von Neumann chose the name Monte Carlo referring to the Monte Carlo Casino in Monaco where Ulam’s uncle would borrow money to gamble [20].

The Monte Carlo simulations are a powerful instrument to obtain information about complex systems but their are possible only with the support of a computing tools. Generally a simulation requires the description of the environment and the material, the starting conditions, physics laws, probability density functions of the physics process involved. All these elements can be inserted with more or less details but the computational power needed can grow very fast if too many variables are in-troduced. Only the developing of faster and faster computers and of grid computing has allowed the diffusion of Monte Carlo simulations.

Some of the modern particles physics experiments require an incredible effort in time and funds to be completed. The choice of materials, geometries and energies involved become crucial for the final apparatus response and it’s really hard to do modifications while the building is in progress or the experiment is already operative, at least without further costs. Monte Carlo simulations become essential in this sector, thanks to their ability to predict particles behaviour under defined conditions and they are greatly used during experiment design phase or during their upgrades. These software are used also during operative phase because the physics models applied in the algorithms have to be compared with the new results collected by the devices.

Several software were created to handle Monte Carlo simulations in particles physics and to extract all the information required by the final users. Some software are developed for specific physics like neutrons, high energies or optics, others are more generic and they include as more models as possible. Physics Monte Carlo simulations can be applied also with smaller devices as in SPECT and PET medical imaging where particles interaction with matter is fundamental for the quality of the images (see Section 2.1). ClearPEM is an example where the design phase of the scanner have been supported by simulations response. EndoTOFPET-US collaboration has decided to apply the same method for the development of the scanner but it required first to run tests in order to decide which simulation software to be used. Two software were chosen to be tested:

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used in PET scanners;

• Geant4 : a software developed for the simulation of several models from high energy physics to optical photons. Widely used in physics community.

A part of this Thesis work was to compare SLitrani (SL) and Geant4 (G4) using from simple to advanced simulations and to understand from their results how to use them in the frame of EndoTOFPET-US collaboration.

4.2 Geant4

GEANT4 is a software to simulate the interaction of particles with matter. It is written in C++ with an object oriented structured. The physics models it uses are very exhaustive and they cover all kind of processes as electromagnetic, hadronic or optical processes. It is possible to simulate a large set of particles with energies from few eV to TeV while materials, volumes and geometries can be well described to reproduce the experimental set-up in a very realistic way. From an interactive point of view, it is possible to extract all kind of parameters regarding the life of a particle during a simulation and simulating a large number of interactions it is possible to obtain a statistic of particles behaviour under the conditions simulated [21].

There are some limitations in this software since in some cases the models are not able to cover all the wide range of energies and the libraries where the physics parameters values are stored are not complete or the level of precision is not really accurate. Behind this project a large community of developers and users keeps working, correcting and upgrading the software. The first production release was finished in 1998 while in 1999 a Geant4 Collaboration was established. A complete manual of Geant4 can be found on its main site [22] while in this work a more detailed description will be provided only for some specific processes.

4.3 SLitrani

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used to show results by mean of ROOT histograms providing different information about photons generated and those that have reached detectors. Initially developed by F.X. Gentit, it has found other developers and several users around the world as it was uploaded on the web [25]. One of the limits of this software is that the specificity in optics is not well balanced in others physics models where imprecisions are encountered.

4.4 Physics behind software

In this work it was studied with particular attention how the simulators manage all the processes regarding optical photons and ray tracing in scintillator crystals. In the following sections I will briefly explain the methods used by G4 and SL to simulate these processes to better understand the simulations results that will be shown in the following chapter.

Absorption length

When the user want to simulate the presence of a volume, for instance the scintillator crystal, both G4 and SL require that a material must be characterized and linked to the volume itself. In this way the software is able to apply the physical properties of the medium to the particles interacting with it. The parameter related to the absorption probability is one of those to be defined. Its value is strictly related to the wave length of the photon crossing the medium and both codes require couples of values absorption length-wave length to simulate this dependency. If a photons with none of the length inserted is generated, the software interpolates the data in order to obtain the missing absorption value.

Boundary processes

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Figure 4.1: Surface treatments simulated. a) polished crystal, b) polished crystal with specular coating, c) polished crystal with diffusive coating, d) polished crystal with spec-ular wrapping and e) polished crystal with diffusive wrapping.

• polished crystal;

• polished crystal with specular coating; • polished crystal with diffusive coating; • polished crystal with specular wrapping; • polished crystal with diffusive wrapping.

Universit`a degli Studi di Milano-Bicocca

Universit`

a degli Studi di Milano-Bicocca

Dipartimento di Fisica

Ph.D. Thesis

OPTIMIZATION AND CHARACTERIZATION OF PET

SCANNERS FOR MEDICAL IMAGING.

Giacomo Cucciati

Prof. Marco Paganoni

Abstract

Acknowledgement

Contents

List of Figures

List of Tables

List of abbreviations

Chapter 1

INTRODUCTION

1.1

Thesis overview

1.2

Crystal Clear Collaboration, a technology

trans-fer.

Chapter 2

POSITRON EMISSION

TOMOGRAPHY

2.1

The technique

2.1.1

The tracer

2.1.2

PET analysis

2.1.3

Coincidence events

2.1.4

Intrinsic spatial resolution limits

2.1.5

Detector design

2.1.6

Sensitivity improvements

2.2

CCC projects

2.2.1

ClearPEM-Sonic

2.2.2

ENDOTOFPET-US

Chapter 3

SCINTILLATOR CRYSTALS

3.1

Scintillation process

3.2

Competitive process to scintillation

3.3

Time response and light yield

3.4

Required properties in scintillator crystals

3.5

Anisotropic crystals

3.5.1

Anisotropy and optical axes

3.5.2

Optical classification

3.5.3

Light propagation in uniaxial crystals

Chapter 4

MONTE CARLO SIMULATION

SOFTWARE

4.1

Introduction: Monte Carlo simulations

4.2

Geant4

4.3

SLitrani

4.4

Physics behind software